
Empirical Results
Overview: From Theory to Evidence
This chapter presents the main empirical findings from our INLA-BYM2 spatial analysis of correctional supervision patterns across Utah. The results demonstrate how environmental conditions, community characteristics, and spatial clustering patterns serve as conversion factors that shape capability formation and correctional outcomes.
Environmental justice emerges as the strongest predictor: A one standard deviation increase in diesel particulate matter is associated with a 494.7% increase in correctional supervision rates, even after controlling for poverty, demographics, and other socioeconomic factors.
1 Main Results: Conversion Factors and Capabilities
1.1 Fixed Effects: Direct Conversion Factor Impacts
1.1.1 Environmental Justice as Primary Conversion Factor
The most striking finding is the overwhelming impact of environmental conditions on correctional supervision outcomes:
- Diesel Particulate Matter: +494.7% increase (95% CI: 239% - 971%)
- Air Quality Index: Significant positive association
- Environmental burden: Compounds other disadvantages
1.1.2 Protective Conversion Factors
Several factors emerged as significant protective influences that enhance capability formation:
Community Engagement & Access
- Census Response Rate: -73.6% (Collective Efficacy)
- Automobile Access: -91.0% (Transportation)
- Bachelor’s Degree: -88.4% (Educational Access)
Economic & Health Security
- Health Insurance: -73.3% (Healthcare Access)
- Employment Rate: -50.0% (Economic Opportunity)
- Homeownership: -40.8% (Housing Stability)
2 Spatial Analysis: Collective Capabilities in Action
2.1 Relative Risk Mapping: Environmental Justice Patterns
The spatial analysis reveals stark geographic inequalities in capability formation: